4x(x-13)=69

Solution for 4x(x-13)=69 equation:

4x(x-13)=69

We move all terms to the left:

4x(x-13)-(69)=0

We multiply parentheses

4x^2-52x-69=0

a = 4; b = -52; c = -69;
Δ = b2-4ac
Δ = -522-4·4·(-69)
Δ = 3808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{238}}{2*4}=\frac{52-4\sqrt{238}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{238}}{2*4}=\frac{52+4\sqrt{238}}{8}
$